Final answer:
The equation that describes the line passing through (-3,1) and is parallel to y = 4x + 1 is y = 4x + 13. This is because parallel lines have the same slope, and after finding the y-intercept using the point (-3,1), we determine that the correct equation is A) y = 4x + 13.
Step-by-step explanation:
The question is asking which equation describes the line that passes through the point (-3,1) and is parallel to the line given by y = 4x + 1. Since parallel lines have the same slope, the slope of the new line will also be 4. To find the y-intercept of the new line, we use the point that the line passes through.
We start with the slope-intercept form of a line, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept. We already know the slope 'm' is 4 (since it must be parallel to y = 4x + 1), so we just need to find 'b' using the point (-3,1) through which the line passes.
Plugging in the values, we get:
1 = (4)(-3) + b
1 = -12 + b
Therefore, b = 13.
The equation of the line is therefore y = 4x + 13.
The correct answer is therefore A) y = 4x + 13, since this line is parallel to y = 4x + 1 (they share the same slope) and it passes through the point (-3,1).